Networking Win7, XP, Win2000, Win98

I have problem networking Win7sp1 with Win2000sp4. Please assume I have to keep Win2k and Win98. I use USB devices and DVDRW as a stop gap solution for now.
I'm tired after a day's un-work. Might as well ask for help.
The problem:
Networking is OK between Win7 and XP PCs, but not between Win7 and Win2k PCs. (Forget Win98 for now.)

I'm referring to hard wired local nets (LAN).
All PCs are with fixed IP addresses between 192.168.1.100-192.168.1.112.
Also want to network Win98se but it is in back burner for now.

Symptoms:
Win7 can see XP PCs and their public, shared folders/files and hard drives.
Win7 can ping Win2000 but Win2k PC does not appear under 'Network' in Win7 folder explorer (Windows Explorer).
Likewise, Win2k can ping Win7 but cannot see Win7 in Windows Explorer under 'Network' folder.
Win2k can see all the XP PCs no problem.
(Besides TCP/IP protocol, I have Netbeui on XP and Win2k also. Note that Win7 has no NetBeui. But XP and Win7 see each other OK, so it is not NetBeui problem.)

Data points:
Win7sp1 is 64-bit Home Premium. The rest Windows are 32 bit systems.
On Win7 and XP, network properties, TCPIPv6 protocol is installed, together with TCPIPv4. TCPIPcv6 was on/off in the tests but has no effect. Dido on QoS on/off.
All PCs have same network group name, such as MYNET, for example.
In all PCs, all software firewalls=off.
For safety, router to outside world is disconnected during tests.
All virus software=off on all PCs. In fact, I uninstalled them as a last ditch!
All PCs are connected via hard wire Cat5e cable to a single switch. No, the switch is not the router. The switch is a standalone 8-port switch.
Yes, had tried another switch, 100Mb/s, 1Gb/s, 10Mb/s oldie even.
Had tried connecting only 2 PCs, Win7 and Win2k, to a single switch.
Had also changed Cat5e cables just be sure.
All PCs can access Internet via the router if the router is connected to the network.
NetBeui on XP and Win2k, installed or uninstalled, has no effect.
All PCs have fixed IP addresses (hence, not relying on DHCP).
Yes, I set Win7 network encryption from 128-bit to 56 bit.
File sharing is on in Win7. No password required.
Yes, some folders in all PCs are set to publicly shared. Access policy on these folders/sub folders is 'Everyone' and 'Full control'.
I also edited Win7 Network Security Policy to enable lower authentication methods. (Had tried both default and the edited policy.)
Anonymous access is off. (Is this THE problem? But then would be a security problem.)

I peruse the Internet for solution also, including MS on networking Win7 and old versions of Windows. (MS never mentions old as Win2k and Win98.) I've read Windows Secrets and forums re networking, including recent Fred Langa articles on networking Win7 and XP.
.....
A light bulb goes up while typing. Will computer name longer than 10 characters affect networking? I know XP and Win7 do not. But DOS type old OSes may impose 8-10 characters limit.
Wait, the Win2K computer name is FamRm, Win7 name is short too, less than 8 characters. So much for a light bulb lighting up. It must be the old incandescent type!

Out of frustration I ask another question:
What is hiding behind the network names in Win7: 'Home Group', "Work' networking, and 'Public' networking?
I read about the explanational description alright. I want to know what they do behind the name, such as security policies, network binding, firewall settings, etc.

Another question:
I now long for the simple NetBeui protocol. (Great for 50 or less PCs.)
If all else fail, can there be a way to install Netbeui on Win7?

NetBeui is much more secure. In Win95, Win2000 days, I bind file sharing to only NetBeui, and not to TCPIP. This single step prevents www access to the local net completely. Yeah, NetBeui is 'noisy'. So what? There are only NetBeui and TCPIP traffics on the wire in home use.
And our ears cannot hear the noise! ... OooK, it's a joke.